I never lived there but I have lived in a couple foreign countries while in the service. My suggestion is to start researching all of your questions. If you decide to go ahead with this you will need to have things preplanned, and have some idea of how to arrange everything otherwise you'll set yourself up for problems and isolation.
I did some browsing on the web to find some info on education there, you would need to do further searching, but here is what I have found. Dubai does have both public and private schooling, but from what I can tell the free schooling is only for citizens. People from other countries can pay to attend private schools, but they have to be enrolled before May or they have to wait for the new year in September. Once you decide to place your child somewhere they are only aloud to change under "special circumstances". Costs vary dramatically. As for English, Dubai does teach Arab but most schools also teach English. Many foreign countries have English as a second language. There were several sites I found with schools that were specifically geared toward English. So both English and Arabic are given which is very good for children. Learning two languages early on is very good for increasing their understanding of language, and increasing connections in the brain. This makes learning later on much easier. Plus at that early age it is much easier for the brain to process and absorb that information.
As for Homeschooling I could not find a lot of official information, but I did find several posts from people who did choose to home-school due to high schooling costs. There are international curriculum's available from many companies that you should be able to have geared toward English while being used in Dubai. Dubai is, as far as I can tell, very advanced compared to many middle eastern cities, and should have accommodations for many of the things you are concerned about.
As I said, you will definitely need to do your research to make sure everything is planned for, that you have a good idea of affordability for things you have to pay for, and that you know the laws, and cultural expectations for the area and nation you will be in. Also make sure you get out and get to know people if you decide to go for it. It is not good to keep yourself isolated in a foreign country. And Dubai should have plenty of English speaking individuals there.